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IMA Journal of Applied Mathematics 1968 4(3):315-319; doi:10.1093/imamat/4.3.315
© 1968 by Institute of Mathematics and its Applications
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The Integration of Bessel Functions

R. A. WALDRON {dagger}

The Marconi Co. Ltd., Research Division Great Baddow, Essex

Starting with the well-known differential and recurrence relations of Bessel functions, a formula is obtained by means of which the nth-order derivative of a Bessel function of order p can be expressed in terms of the Bessel function of order p and its first derivative, the function and its derivative being multiplied by polynomials in 1/x, x being the argument. By using the method in reverse, the integral of a Bessel function can be expressed in terms of the Bessel function and its derivative, which are multiplied by series in x if p is even, or polynomials in 1/x if p is odd. These formulae are more convenient for computation than the well-known formulae involving series of Bessel functions.


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